# rational_funcs(n) [osx man page]

math::rationalfunctions(n) Math math::rationalfunctions(n)__________________________________________________________________________________________________________________________________________________NAME

math::rationalfunctions - Polynomial functionsSYNOPSIS

package require Tcl ?8.4? package require math::rationalfunctions ?1.0.1? ::math::rationalfunctions::rationalFunction num den ::math::rationalfunctions::ratioCmd num den ::math::rationalfunctions::evalRatio rational x ::math::rationalfunctions::addRatio ratio1 ratio2 ::math::rationalfunctions::subRatio ratio1 ratio2 ::math::rationalfunctions::multRatio ratio1 ratio2 ::math::rationalfunctions::divRatio ratio1 ratio2 ::math::rationalfunctions::derivPolyn ratio ::math::rationalfunctions::coeffsNumerator ratio ::math::rationalfunctions::coeffsDenominator ratio_________________________________________________________________DESCRIPTION

This package deals with rational functions of one variable: o the basic arithmetic operations are extended to rational functions o computing the derivatives of these functions o evaluation through a general procedure or via specific procedures)PROCEDURES

The package defines the following public procedures: ::math::rationalfunctions::rationalFunction num den Return an (encoded) list that defines the rational function. A rational function 1 + x^3 f(x) =1 + 2x + x^2 can be defined via: set f [::math::rationalfunctions::rationalFunction [list 1 0 0 1] [list 1 2 1]] list num Coefficients of the numerator of the rational function (in ascending order) list den Coefficients of the denominator of the rational function (in ascending order) ::math::rationalfunctions::ratioCmd num den Create a new procedure that evaluates the rational function. The name of the function is automatically generated. Useful if you need to evaluate the function many times, as the procedure consists of a single [expr] command. list num Coefficients of the numerator of the rational function (in ascending order) list den Coefficients of the denominator of the rational function (in ascending order) ::math::rationalfunctions::evalRatio rational x Evaluate the rational function at x. list rational The rational function's definition (as returned by the rationalFunction command). order) float x The coordinate at which to evaluate the function ::math::rationalfunctions::addRatio ratio1 ratio2 Return a new rational function which is the sum of the two others. list ratio1 The first rational function operand list ratio2 The second rational function operand ::math::rationalfunctions::subRatio ratio1 ratio2 Return a new rational function which is the difference of the two others. list ratio1 The first rational function operand list ratio2 The second rational function operand ::math::rationalfunctions::multRatio ratio1 ratio2 Return a new rational function which is the product of the two others. If one of the arguments is a scalar value, the other ratio- nal function is simply scaled. list ratio1 The first rational function operand or a scalar list ratio2 The second rational function operand or a scalar ::math::rationalfunctions::divRatio ratio1 ratio2 Divide the first rational function by the second rational function and return the result. The remainder is dropped list ratio1 The first rational function operand list ratio2 The second rational function operand ::math::rationalfunctions::derivPolyn ratio Differentiate the rational function and return the result. list ratio The rational function to be differentiated ::math::rationalfunctions::coeffsNumerator ratio Return the coefficients of the numerator of the rational function. list ratio The rational function to be examined ::math::rationalfunctions::coeffsDenominator ratio Return the coefficients of the denominator of the rational function. list ratio The rational function to be examined------------REMARKS ON THE IMPLEMENTATION

The implementation of the rational functions relies on the math::polynomials package. For further remarks see the documentation on that package.BUGS, IDEAS, FEEDBACKThis document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category math :: rationalfunctions of the Tcllib SF Trackers [http://sourceforge.net/tracker/?group_id=12883]. Please also report any ideas for enhance- ments you may have for either package and/or documentation.KEYWORDS

math, rational functionsCATEGORY

MathematicsCOPYRIGHT

Copyright (c) 2005 Arjen Markus <arjenmarkus@users.sourceforge.net>math1.0.1 math::rationalfunctions(n)